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Quantification and evaluation of uncertainty in active buckling control of a beam-column subject to dynamic axial loads

Schäffner, Maximilian Frederic (2019):
Quantification and evaluation of uncertainty in active buckling control of a beam-column subject to dynamic axial loads.
Darmstadt, Technische Universität, [Online-Edition: https://tuprints.ulb.tu-darmstadt.de/8652],
[Ph.D. Thesis]

Abstract

Slender beam-columns in lightweight mechanical load-bearing structures are sensitive to failure by buckling when loaded by compressive axial loads. The maximum bearable axial load of a beam-column is considerably reduced by uncertainty in the material, geometry, loading or support properties, but may be increased by active buckling control. So far, studies on active buckling control have investigated academic beam-column systems with rectangular cross-sections, high slenderness ratios and small critical buckling loads as well as (quasi-)static axial loads. In this thesis, active buckling control of a practical beam-column system with circular cross-section, relatively low slenderness ratio and relatively high critical buckling load as well as dynamic axial loads, as opposed to the academic beam-column systems is investigated. The goal is to increase the maximum bearable axial load and reduce uncertainty in the buckling behavior. For the latter, probabilistic uncertainty in the maximum bearable axial loads and lateral deflections of the passive and active beam-column systems is quantified and evaluated experimentally.

This thesis opens with a review of the background in static and dynamic passive buckling and the previous research on active buckling control. The concept for active buckling control uses innovative piezo-elastic supports with integrated piezoelectric stack actuators. A mathematical linear parameter-varying (LPV) model of the axially loaded beam-column system with electrical components accounts for the axial load-dependency of the lateral dynamic behavior. The model is calibrated with experimental data and then used to design an LPV controller, in particular a gain-scheduled H_∞ controller, which guarantees stability and robust performance for the entire operation range of axial loads. Passive buckling and active buckling control are investigated in an experimental test setup with slowly increasing quasi-static and step-shaped dynamic axial loads. Probabilistic uncertainty in the maximum bearable quasi-static axial loads and the lateral deflections for dynamic axial loads due to component variations in a representative sample of beam-column systems is investigated experimentally. The experimental results are quantified and evaluated by three-parameter WEIBULL distributions and compared for the passive and active beam-column systems with respect to their most likely values and variability.

The proposed gain-scheduled H_∞ buckling control stabilizes the beam-column system in arbitrary lateral direction. For quasi-static axial loads, the most likely maximum bearable axial loads increase by 29% and the variability reduces by 70% when comparing the passive and active beam-column system. For dynamic axial loads, the most likely lateral deflections reduce by up to 87% and the variability reduces by up to 90%. Overall, the results of this thesis contribute to the application of active buckling control in practical truss structures.

Item Type: Ph.D. Thesis
Erschienen: 2019
Creators: Schäffner, Maximilian Frederic
Title: Quantification and evaluation of uncertainty in active buckling control of a beam-column subject to dynamic axial loads
Language: English
Abstract:

Slender beam-columns in lightweight mechanical load-bearing structures are sensitive to failure by buckling when loaded by compressive axial loads. The maximum bearable axial load of a beam-column is considerably reduced by uncertainty in the material, geometry, loading or support properties, but may be increased by active buckling control. So far, studies on active buckling control have investigated academic beam-column systems with rectangular cross-sections, high slenderness ratios and small critical buckling loads as well as (quasi-)static axial loads. In this thesis, active buckling control of a practical beam-column system with circular cross-section, relatively low slenderness ratio and relatively high critical buckling load as well as dynamic axial loads, as opposed to the academic beam-column systems is investigated. The goal is to increase the maximum bearable axial load and reduce uncertainty in the buckling behavior. For the latter, probabilistic uncertainty in the maximum bearable axial loads and lateral deflections of the passive and active beam-column systems is quantified and evaluated experimentally.

This thesis opens with a review of the background in static and dynamic passive buckling and the previous research on active buckling control. The concept for active buckling control uses innovative piezo-elastic supports with integrated piezoelectric stack actuators. A mathematical linear parameter-varying (LPV) model of the axially loaded beam-column system with electrical components accounts for the axial load-dependency of the lateral dynamic behavior. The model is calibrated with experimental data and then used to design an LPV controller, in particular a gain-scheduled H_∞ controller, which guarantees stability and robust performance for the entire operation range of axial loads. Passive buckling and active buckling control are investigated in an experimental test setup with slowly increasing quasi-static and step-shaped dynamic axial loads. Probabilistic uncertainty in the maximum bearable quasi-static axial loads and the lateral deflections for dynamic axial loads due to component variations in a representative sample of beam-column systems is investigated experimentally. The experimental results are quantified and evaluated by three-parameter WEIBULL distributions and compared for the passive and active beam-column systems with respect to their most likely values and variability.

The proposed gain-scheduled H_∞ buckling control stabilizes the beam-column system in arbitrary lateral direction. For quasi-static axial loads, the most likely maximum bearable axial loads increase by 29% and the variability reduces by 70% when comparing the passive and active beam-column system. For dynamic axial loads, the most likely lateral deflections reduce by up to 87% and the variability reduces by up to 90%. Overall, the results of this thesis contribute to the application of active buckling control in practical truss structures.

Place of Publication: Darmstadt
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Research group System Reliability, Adaptive Structures, and Machine Acoustics (SAM)
16 Department of Mechanical Engineering > Research group System Reliability, Adaptive Structures, and Machine Acoustics (SAM) > Development, modelling, evaluation, and use of smart structure components and systems
16 Department of Mechanical Engineering > Research group System Reliability, Adaptive Structures, and Machine Acoustics (SAM) > Characterization, evaluation, and control of the reliability of mechanical systems
DFG-Collaborative Research Centres (incl. Transregio)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 805: Control of Uncertainty in Load-Carrying Structures in Mechanical Engineering
Date Deposited: 19 May 2019 19:55
Official URL: https://tuprints.ulb.tu-darmstadt.de/8652
URN: urn:nbn:de:tuda-tuprints-86527
Referees: Melz, Prof. Dr. Tobias and Klingauf, Prof. Dr. Uwe
Refereed / Verteidigung / mdl. Prüfung: 11 December 2018
Alternative Abstract:
Alternative abstract Language
Schlanke Balken in mechanischen Leichtbaustrukturen sind empfindlich gegenüber dem Versagen durch Knicken infolge axialer Druckkräfte. Die maximal ertragbare Axiallast eines Balkens wird durch Unsicherheit in Material, Geometrie, Belastung oder Lagerung erheblich reduziert, kann aber durch aktive Stabilisierung erhöht werden. Bislang wurde die aktive Stabilisierung jedoch nur für akademische Balkensysteme mit Rechteckquerschnitt, hohen Schlankheitsgraden und kleinen kritischen Knicklasten sowie (quasi-)statischer Axiallast untersucht. In dieser Arbeit wird die aktive Stabilisierung für ein realitätsnahes Balkensystem mit Rundquerschnitt, relativ geringem Schlankheitsgrad und relativ hoher kritischer Knicklast sowie dynamischer Axiallast untersucht. Das Ziel ist es, die maximal ertragbare Axiallast zu erhöhen und die Unsicherheit im Knickverhalten zu reduzieren. Dafür wird die probabilistische Unsicherheit in den maximal ertragbaren Axiallasten und den lateralen Auslenkungen des passiven und aktiven Balkensystems experimentell quantifiziert und bewertet. Zu Beginn dieser Arbeit werden die mechanischen Grundlagen des statischen und dynamischen passiven Knickens vorgestellt und ein Überblick über die bisherigen Untersuchungen zur aktiven Stabilisierung gegeben. Das neu vorgestellte Konzept zur aktiven Stabilisierung nutzt innovative piezo-elastische Lager mit integrierten piezoelektrischen Stapelaktuatoren. Ein mathematisches linear Parameter-veränderliches (LPV) Modell des axial belasteten Balkensystems mit elektrischen Komponenten berücksichtigt die Axiallastabhängigkeit des lateralen dynamischen Balkenverhaltens. Das Modell wird mit experimentellen Daten kalibriert und anschließend für den Entwurf einer LPV-Regelung, im speziellen einer gain-scheduled H_∞ Regelung, welche Stabilität und robuste Performance für den gesamten Bereich der axialen Lasten garantiert, verwendet. Das passive Knicken und die aktive Stabilisierung werden in einem experimentellen Versuchsstand mit langsam ansteigenden quasi-statischen und stufenförmigen dynamischen Axiallasten untersucht. Die probabilistische Unsicherheit in den maximal ertragbaren quasi-statischen Axiallasten und in den lateralen Balkenverformungen bei dynamischen Axiallasten wird infolge von Komponentenvariationen in einer repräsentativen Stichprobe von Balkensystemen untersucht. Die experimentellen Ergebnisse werden durch dreiparametrige WEIBULL-Verteilungen quantifiziert und ausgewertet und für das passive und aktive Balkensystem hinsichtlich ihrer wahrscheinlichsten Werte und Streuungen verglichen. Die vorgeschlagene gain-scheduled H_∞ Regelung stabilisiert den axial belasteten Balken in beliebige laterale Richtungen. Für quasi-statische Axiallasten erhöht sich die wahrscheinlichste maximal ertragbare Axiallast um 29 % und die Streuung verringert sich um 70 %. Für dynamische Axiallasten reduzieren sich die wahrscheinlichsten lateralen Auslenkungen um bis zu 87 % und die Streuung verringert sich um bis zu 90 %. Insgesamt tragen die Ergebnisse dieser Arbeit zur Anwendung der aktiven Stabilisierung in realen Tragwerkstrukturen bei.German
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